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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 34C / a

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2024 ii Paper 2 34C
Created 2026-09-23 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
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a
The stated operators form a Lax pair when the KdV equation is equivalent to
∂t​L=[L,A]=LA−AL​.
(1)
Indeed, if Lϕ=k2ϕ, differentiation and this identity show
(L−k2)(Aϕ+∂t​ϕ)=([L,A]−Lt​)ϕ=0.
(2)
Thus ∂t​+A preserves every spectral eigenspace, which is the Isospectral Lax equation formulation.

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